Dial-up customers need to contact Orange during the next fortnight if they don't want to upgrade to the ADSL connection.
A spokesman who talked to IS Preview.co.uk said the decision to close the service will allow the company to invest in new products "more effectively".
"We believe that broadband provides our customers with more benefits and greater value for money than AnyTime dial-up. In a lot of cases, AnyTime customers will be paying less than they were before."
Orange UK is a subsidiary of France Telecom, which is one of the largest telecommunications companies in the world with around 159 million customers worldwide.
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